Statistical Benefits of Value at Risk with Long Memory

Are there substantial improvements associated with the use of long memory models in the computation of value-at-risk (VAR)? The performance of the GARCH and the ARFIMA models, the latter estimated using daily variance obtained from high-frequency data, are compared on various criteria. The results show that the long memory model provides a superior performance in terms of multi-step point forecasting. Allowing for time-varying variance of the realized variance process in the context of an ARFIMA–FIGARCH model also substantially improves VAR forecasting.